MELBOURNE, Australia -- Novak Djokovic was all but perfect in his second-round match Wednesday against Ryan Harrison, beating the 20-year-old American 6-1, 6-2, 6-3 to stay on track for his third consecutive Australian Open title and the fourth of his career.

Maria Sharapova was even more convincing a few hours earlier, winning 6-0, 6-0 for the second time in two matches to set up a third-round encounter with Venus Williams.

Williams beat Alize Cornet 6-3, 6-3 in the match preceding the Djokovic-Harrison encounter at Rod Laver Arena, which will be the likely venue for her big matchup Friday against Sharapova.

Reigning French Open champion Sharapova holds a 4-3 edge in career meetings, but Williams has won both of their meetings at Grand Slam tournaments -- at Wimbledon in 2005 and 2007.

Venus' sister Serena, playing in the other half of the draw, had the day off Wednesday and was able to rest the right ankle she injured in her first-round match. She's set to play Garbine Muguruza on Thursday as she pursues her own sequence of three. She won Wimbledon and the U.S. Open last year and is aiming for a third major in a row.

Djokovic, a loser in the U.S. Open final last year to Andy Murray, looks like he wants to atone for that defeat. He was relentless in beating the overmatched Harrison, winning the first set in just 20 minutes and the match in 1½ hours while making just 16 unforced errors.

"I tried to focus from the start," Djokovic said. "Obviously, I knew he had nothing to lose, he's going to come out and hit big serves. Pity for him, I don't think he played his best."

Sharapova did, particularly for someone who has precious little match "toughness" heading into the Australian Open. The second-seeded Russian beat Japan's Misaki Doi by the double-bagel score in just 47 minutes, her second consecutive match at Melbourne Park in which her opponent failed to win a game. Doi won only 15 points.

Sharapova, last year's Australian Open runner-up, pulled out of the Brisbane International with a right collarbone injury two weeks ago and had not played a competitive match this year until her 6-0, 6-0 win over fellow Russian Olga Puchkova in the first round Monday.

She is the first woman to post consecutive 6-0, 6-0 scorelines at a Grand Slam since Wendy Turnbull at the Australian Open in 1985.

"I've been playing really aggressive and doing the right things," Sharapova said. "It's not easy to be up so much because you can have a few letdowns. You just have to try to concentrate. My job is to make it as easy as possible."

Venus Williams took advantage of Cornet's double-fault to end the first set.

"Tennis ... is about winning when it's not your best day," the 25th-seeded Williams said. Next up "I'm playing against Maria. I'm going to have to be at my best against her."

The final match of Wednesday's session on the center court was disappointing, though not wholly unexpected, for the home crowd and Australia's top-ranked female player.

Ninth-seeded Samantha Stosur, who has spoken of her anxiety over playing in front of her home fans, served twice for the match but double-faulted on match point in a 6-4, 1-6, 7-5 loss to China's Zheng Jie.

"It was a bit of a choke," Stosur admitted. "Obviously it's a hard one to take when you get yourself into a winning position and you lose five games straight."

Stosur, who had nine double-faults and 56 unforced errors, has never gone beyond the fourth round at her home Grand Slam, lost in the first round last year and also lost in her first matches at warm-up tournaments this year in Brisbane and Sydney.

"I needed to keep fighting and enjoy the match," Zheng said. "It's amazing I came back."

Earlier, fourth-seeded Agnieszka Radwanksa extended the year's best winning streak to 11 matches. She eased into the third round with a 6-3, 6-3 victory over Romania's Irina-Camelia Begu and remains unbeaten this year, including titles at warm-up tournaments this month at Auckland and Sydney.

"I can play even better," said Radwanska, who lost last year's Wimbledon final to Serena Williams. "I didn't really expect I could win that many matches in a row, and hopefully I can keep going."

Her last two trips to the Australian Open have ended in quarterfinal losses to the eventual champion -- Kim Clijsters in 2011 and Victoria Azarenka last year.

With top-ranked Azarenka and Serena Williams on the other half of the draw, Radwanska's main obstacles to reaching the final are 2011 French Open champion Li Na, who beat Olga Goortsova of Belarus 6-2, 7-5 to reach the third round, and potential semifinal rivals Sharapova or No. 5 Angelique Kerber, who advanced with a 6-3, 6-1 win over Lucie Hradecka.

Serena Williams, who has lost only one match since her first-round exit at the French Open last year, canceled an outdoor practice session and moved it indoors to test out her sore ankle.

No. 20 Sam Querrey advanced when fellow American Brian Baker retired in the second set with a right knee injury and next plays No. 15 Stanislas Wawrinka.

Baker, who returned to the tour last year after missing almost six seasons with a variety of injuries, won a first-set tiebreaker and was level at 1-1 on serve in the second. He was later pushed from Court 6 in a wheelchair.

Tournament organizers said that Baker had a torn meniscus and is expected to be out about four months.

"Yeah, he's the last person that deserves anything like that with his five or six surgeries already," Querrey said.